Abstract. Vietnamese mathematics teachers continue to waste time to equip students which
specified in the textbook and give them the process. Students are not encouraged to discover
the challenging exercises that require practicable problem solving ability and complicated
thinking formulas, so they are not interested in Math. The problem is that:
- Why is it so difficult to teach Mathematics using practical situations?
- Can Vietnamese teachers teach Mathematics using practical situations?
- How can high school math teachers learn to teach Mathematics using practical situations?
To answer three above questions and figure out solutions for teacher to organize
teaching case associated with practical situations, this article shows several researches and
recommendations.

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JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1075.2015-0290
Educational Sci., 2015, Vol. 60, No. 8A, pp. 236-242
This paper is available online at
SOLUTION FOR TEACHER IN ORGANISING LEARNING CASE
ASSOCIATED WITH PRACTICAL SITUATIONS IN HIGH SCHOOL
Chu Cam Tho
Faculty of Mathematics and Informatics, Hanoi National University of Education
Abstract.Vietnamese mathematics teachers continue to waste time to equip students which
specified in the textbook and give them the process. Students are not encouraged to discover
the challenging exercises that require practicable problem solving ability and complicated
thinking formulas, so they are not interested in Math. The problem is that:
- Why is it so difficult to teach Mathematics using practical situations?
- Can Vietnamese teachers teach Mathematics using practical situations?
- How can high school math teachers learn to teach Mathematics using practical situations?
To answer three above questions and figure out solutions for teacher to organize
teaching case associated with practical situations, this article shows several researches and
recommendations.
Keyword: Mathematics teaching method, practical situations, high school, teaching case,
learning case.
1. Introduction
In the real life, mathematics knowledge is frequently used. Having solid mathematics
background helps people calculate or estimate rapidly and have logical thinking to solve well not
only academic problems but also daily ones.
In high school, besides being useful in learning Maths, Physics, Biology, Chemistry,
mathematics knowledge also provides students many chances in forming and developing key
competencies, namely calculating, logical thinking, problem solving, self-study, communication,
cooperating, self-control and technology applying skill (Tran Kieu and co-authors, International
senimar of capacity orientation training’s report, Ministry of Education and Training, 2012)
Recently, in teaching method innovation wave helps people realize the goal of teaching
which aims to bring theory into practice. However, in mathematics teaching, the results of that
wave did not meet the requirement. Teachers still did not aware the role of Maths and the influence
of teaching methods in student’s learning way. Teachers still waste time to repeat students which
specified in the textbook and give them the processed exercises (Nghi Bui Van, 2013). Students
have no chance in discovering the challenging exercises that require practicable problem solving
ability and complicated thinking formulars, so they are not interested in Maths lessons (Tran Vui,
2010a, 2010b)
Received: 15/7/2015. Accepted: 01/9/2015
Contact: Chu Cam Tho, e-mail: camtho@hnue.edu.vn
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Solution for teacher in organising learning case associated with practical situation in high school
The problem is that :
- What are the difficulties that impact on Mathematics teaching method that associated with
practical situations?
- Are teachers able to organise Mathematics teaching cases that associated with practical
situations?
- How to help Maths teachers in organising Mathematics teaching cases that associated with
practical situations in highschool?
To answer three above questions and figure out solutions for teacher to organize
teaching case associated with practical situations, this article shows several researches and
recommendations.
2. Researching result
2.1. Rationale of Mathematics teaching associated with practice requirements
UNESCOCultural and Educational program of The United Nations has set the 21st century
goal of education is learning to know, learning to do, learning to live together, and learning to be.
Therefore, high school education has to create learning activities that be applicable in real life,
put learning from practice as main content and teaching method. Recently, educational policy
makers all over the world start reforming Mathematics education by reforming content, program
and student’s learning method (Garet and co-authors, 2001). These reforming efforts focus on
developing problem solving capacity (PSC), Mathematics reflecting and communicating skill in
order to help students achieve their both deep and wide Mathematics academic knowledge and gain
more career and learning opportunities in the future (National Council of Teachers of Mathematics
(NCTM), 2000).
Figure 1. Model of Mathematics problem solving capacity (Wu, 2003)
According to the above analysis, the capacities that Mathematics education programs care
about more or less relate to Mathematics applying in practice, such as problem posing and solving
237
Chu Cam Tho
capacity (Figure 1) and modeling capacity.
On another hand, Mathematics history demonstrated that firstly, mathematics knowledge
came from practice researching and even when it is abstract, it still come for serving reality.
If students cannot realize connection of Maths and reality, high school education will lose its
role; this was generalized in mathematics characteristics analysis (Kim Nguyen Ba, Mathematics
teaching method, 2006)
One of recent researches in teaching method associated with practice is Mathematics
teaching through survey. This is a teaching approach formed and popular in Education researchers
and Maths teachers Association in the UK from 1960s; and was recognized as an effective one
since it allows students have an exciting and highly interactive learning environment (Bailey, 2007;
Jaworski, 1994; Orton and Frobisher, 1996; Ponte, 2007; Vui Tran, 2010; Duyen Nguyen Thi,
2013)
Nowadays, International student assessment programs highly appreciate Mathematics
knowledge practice applicable capacity (PISA, IB, so on). It is a challenge for Vietnamese
Education on the integration way to ensure training objectives and meet social requirements.
2.2. Difficulties in teaching aims to apply Mathematics in practical in high
school
In 2012, we conducted a survey of 216 secondary school teachers in Hanoi and Quang Ninh
about Mathematics teaching activities. The result is that, in 216 respondents, there are 100% asked
people said that almost all (80 – 85%) teaching hours spent on calculating activities, included
exercise checking and assigning; 197 respondents (91.2%) said they usually skip exercises,
practical model exercises, because they themselves lack of documents, experiences and they don’t
think it’s useful for students examinations. Some others think that their students don’t like to do
practice related exercises and do not recognize the applicable role of Mathematics into real life.
On another hand, while studying some documents of Mathematics teachers and lesson
assessment guiding of Hanoi Education and Training Department and Quang Ninh’s one, we found
that the criteria “experience innovation” and “practical related teaching” were still not be cared.
Compared with some others, namely having excellent students, having fulfillment profiles and
recorded documents, “innovative content and teaching methods” is hard to achieve by teacher.
While taking part in assessing teachers experience innovation, we recognized that they still choose
the “traditional” problems to write like: practicing Mathematics task solving skill, focusing on
one type of exercise. Even if some contest was held in order to improve applying background
knowledge on practice capacity that authors joined namely The Creative Teacher by teacher
National Office and Microsoft; multi – subjects knowledge application and integrating teaching by
Secondary Education Department – Ministry of Education and Training; or Science for students,
there are rarely qualified Mathematics entries appeared.
Vietnam has joined the PISA, but the impact of these contests on Mathematics teaching and
learning is not high. However, no denial that open – Mathematics task style and practice – related
one are advantages. These styles and contents usually create excitement and help students be more
active in learning.
2.3. Measure that help teachers design practice related teaching situation
In this article, the measurements was drawn while helping 4 teachers, namely: Tam Dang
Thi Minh – teacher of Hanoi Alpha School, Hai Nguyen Huu – postgraduate student, 22th course
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Solution for teacher in organising learning case associated with practical situation in high school
of Hanoi National University of Education (HNUE), Dung Nguyen Thuy – teacher of Trung
Vuong Secondary School, Tham Tran Thi – class 10, Uong Bi Education College, part-time course
student, design their practice related teaching situation. We take some measures with purposes:
- Helping teachers recognise the role of Maths and applying Mathematics knowledge in
practice.
- Analysing suitable lesson aim for students.
- Researching and thinking about practice related knowledge and situation when teaching
Maths regularly.
- Design and organise practice related teaching situation well.
The first: Media helps teachers recognize the role of Maths and applying Mathematics
knowledge in practice
Through direct discussion with the teachers above, we found that, teachers often lack of
motivation and confidence in the properly implement teaching aim and method. Therefore, firstly,
we want to help teachers rebuild teaching motivation by supplying scientific information and
practical limitation due to the deviation from target teaching. The result is that teachers, who took
part in our plan, were impressed and they found another practical reality beside what they usually
do (said, Tham Tran Thi and Hai Nguyen Huu). We set up a closed group on social network and
a website ( to share teaching ideas, documents and experience. For 2 years, our
members have shared on there and they no longer feel alone or differential. At the same time, these
experiences helps them overcome difficulties. The result is:
Tham Tran Thi selected her graduation thesis and experience innovation related the content:
“designing PISA exercises for secondary school students”.
Dung Le Thuy took part in the Creative teacher, and was in the final round. She also be an
impressive teacher when taking a sample lesson in front of whole school and applying reforms on
Maths, Physics and advisor’s work what she has never done before.
Hai Nguyen Huu chose the graduation thesis content about “designing practice related
teaching situation and training modeling capacity for students”.
Tam Dang Thi Minh has applied knowledge of learning project organizing for 6, 7 grade
students in Alpha school since early teaching period.
The second: Applying Lesson study model and creative Science and Technology
technique in order to help teachers design an effective lesson.
According to Jica organization’s researches (Saito co-authors, 2007; Lewis, 2009), before
building professional activity model, teachers would be helped to have good study lesson, it is
the sufficient condition to not only be confident but also like and be convinced of the researching
problem’s benefits.
We also refer to the study of serveral concerned contents include open problem and
mathematics survey. Thanks to the research of Vui Tran (2010), Duyen Nguyen Thi (2012),
Handbook PISA (Ministry of Education and Training) we gathered into a material to help teachers
with more resources and scientific basis knowledge.
In order to help teachers design an effective lesson, we suggest that teachers answer
questionnaires:
- Who will learn this lesson?
- What do students learn this lesson for?
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Chu Cam Tho
- Currently, how do teachers teach this lesson?
- Are we able to improve the way of teaching this lesson in order to accord with learner?
- What does practical situation related to this lesson?
Besides, we used brainstorming and the technique of focal objects (Dung Phan, 2007; Tho
Chu Cam, 2010) in order to help teachers more creatively. It is worth sharing that brainstorming
being conducted via Groups on social network not only help teachers solve the difficulties of time
and space (groups of teachers in many different schools) but the advantages are that all feedback
is true. Focal objects paid attention were contents related to the last question "What does practical
situation relate to this lesson?" Using these technique, teachers were more confident, opener in
thinking and were able to suggest more practical situations. For example, firstly, Hai had never
suggested any practical situation related to integral for two days. But after focusing in images
associated with "the tip" in solid revolution, Hai spent time observing and he recognized hills in
Nghia Do Park or reservoir of hydroelectric may be a good suggestion for his lesson. Then, Hai
discussed with other teachers in order to improve his lesson. When Dung had difficulty in finding
application of the highest common factor (HCF) and lowest common multiple (LCM) in practice,
teachers in Groups took ideas grouping, planting vegetables in plot, organizing party table (Tham),
(Tam), ...
Figure 2. The adjusting mechanism of the modeling process
(Nam Nguyen Danh, Trung Tran, Cuong Dang Xuan, Hong Nguyen Van, 2011)
Here is a model that describes the adjusting mechanism to simplify the modeling practical
situations into learning situations (Figure 2).
Another task is designing learning activities, however this is difficult for teacher. We
suggested teachers should use the technique “think about students” in three steps as follows:
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Solution for teacher in organising learning case associated with practical situation in high school
(1) Choose three students from different groups of level and character, then design learning
activities for each of them.
(2) Put the remaining students into three groups. At this stage, teachers need to predict the
difficulties which students can encounter.
(3) Design activities for students to overcome the difficulties.
We encourage teachers to use that technique combines with two suitable techniques for
practical situation teaching, namely four corners and learning in station. The creation of the corners
and the station will ensure the aims: divided level, self - control learner and create excitement for
students.
After completing design lessons, teachers in Group on social network comment on it.
Teachers edit lesson plans before teaching experiment. We record teaching experiment videos and
upload them to social networks to share them with other teachers.
3. Conclusion
For more than a year of implementation, the team has achieved significant results. We have
built the teaching and learning situations such as teaching projects: "Bridge" theme associated with
three straight points – Mathematics 6, “Business” associated with the topic Statistics - Algebra 7,
Project "Occupational Choice" - Algebra 10, "Graphs of quadratic functions" - Algebra 10, HCF
– LCM - Mathematics 6, "Explorers of the Human Body" - joint project Biology - Mathematics 6,
"Applications of integrals - Analysis 12,"Should we play lots? "- Probability, Algebra and Calculus
11.
Although the Ministry of Education and Training require teachers to pay attention and
perform design learning activities associated with practical situation. However, from the above
studies, we found that the design of situations associated with the practice is not an easy task for
teachers. This is not new in the history of education in Vietnam, but for teachers, the teaching
routine and pressure from the examinations has created certain obstacles. The results from case
studies of four teachers showed that, if teachers have positive and frequent helped hand, they
can improve their teaching in order to create the circumstances associated with the practice, in
accordance with local conditions and their own ability.
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